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Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs

Sahimel Azwal, Sulaiman (2018) Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs. PhD thesis, Universiti Malaysia Pahang.

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Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs - Table of contents.pdf - Accepted Version

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Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs - Abstract.pdf - Accepted Version

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Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs - References.pdf - Accepted Version

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Abstract

The nonabelian tensor product is defined for a pair of groups which act on each other provided the actions satisfying the compatibility conditions. Different pairs of compatible actions will give different nonabelian tensor products. Thus, in this research, the maximum number of different nonabelian tensor products between two groups is found by determining the exact number of compatible pairs of actions and focusing only on the finite cyclic 2-groups. This research starts with determination of the exact number of compatible pairs of actions by using the necessary and sufficient conditions of finite cyclic 2-groups to act compatibly on each other. In order to find the number of compatible pairs of actions of finite cyclic 2-groups, the compatible action graph is introduced. Then, some properties of he compatible action graph and a subgraph of the compatible action graph are determined.

Item Type: Thesis (PhD)
Additional Information: Thesis (Doctor of Philosophy) -- Universiti Malaysia Pahang – 2018, SV: DR. MOHD SHAM BIN MOHAMAD, NO. CD: 11625
Uncontrolled Keywords: Nonabelian tensor; compatible action graphs; cyclic 2-groups
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Faculty/Division: Faculty of Industrial Sciences And Technology
Depositing User: Mrs. Sufarini Mohd Sudin
Date Deposited: 30 May 2019 01:52
Last Modified: 30 May 2019 01:52
URI: http://umpir.ump.edu.my/id/eprint/24716
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